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Volumn 64, Issue 8, 2006, Pages 1757-1797

Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms

Author keywords

Decay rates; Localized damping; Neumann boundary conditions; Nonlinear dissipation; Potential well; Source; Stability; Wave equation

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; DAMPING; ELECTRON ENERGY LEVELS; LINEAR EQUATIONS; NONLINEAR EQUATIONS; THEOREM PROVING;

EID: 32344439207     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.07.024     Document Type: Article
Times cited : (110)

References (33)
  • 1
    • 32344437781 scopus 로고    scopus 로고
    • On convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems
    • to appear
    • F. Alabeau, On convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems, Appl. Math. Optim., to appear.
    • Appl. Math. Optim.
    • Alabeau, F.1
  • 3
    • 14844365160 scopus 로고    scopus 로고
    • Decay of solutions of the wave equation with arbitrary localized nonlinear damping
    • M. Bellassoued Decay of solutions of the wave equation with arbitrary localized nonlinear damping J. Differential Equations 211 2005 305 332
    • (2005) J. Differential Equations , vol.211 , pp. 305-332
    • Bellassoued, M.1
  • 5
    • 11244330804 scopus 로고    scopus 로고
    • Uniform decay rates of solutions to a system of coupled PDE's with nonlinear internal dissipation
    • F. Bucci Uniform decay rates of solutions to a system of coupled PDE's with nonlinear internal dissipation Differential Integral Equations 16 2003 865 896
    • (2003) Differential Integral Equations , vol.16 , pp. 865-896
    • Bucci, F.1
  • 6
    • 3042680695 scopus 로고    scopus 로고
    • Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
    • M. Cavalcanti, V. Cavalcanti, P. Martinez, Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term, J. Differential Equations (2004).
    • (2004) J. Differential Equations
    • Cavalcanti, M.1    Cavalcanti, V.2    Martinez, P.3
  • 7
    • 0000765901 scopus 로고
    • A note on boundary stabilization of the wave equation
    • G. Chen A note on boundary stabilization of the wave equation SIAM J. Control Optim. 19 1981 106 113
    • (1981) SIAM J. Control Optim. , vol.19 , pp. 106-113
    • Chen, G.1
  • 8
    • 0036908993 scopus 로고    scopus 로고
    • On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation
    • I. Chueshov, M. Eller, and I. Lasiecka On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation Comm. PDE 27 2002 1901 1951
    • (2002) Comm. PDE , vol.27 , pp. 1901-1951
    • Chueshov, I.1    Eller, M.2    Lasiecka, I.3
  • 9
    • 0000028946 scopus 로고
    • Existence of solutions of the wave equation with nonlinear damping and source term
    • V. Georgiev, and G. Todorova Existence of solutions of the wave equation with nonlinear damping and source term J. Differential Equations 109 1994 295 308
    • (1994) J. Differential Equations , vol.109 , pp. 295-308
    • Georgiev, V.1    Todorova, G.2
  • 12
    • 0001963160 scopus 로고
    • Semilinear hyperbolic problems in bounded domains
    • Harwood Gordon Breach, New York
    • A. Haraux, Semilinear Hyperbolic Problems in Bounded Domains, Mathematical Reports, vol. 3, Harwood Gordon Breach, New York, 1987.
    • (1987) Mathematical Reports , vol.3
    • Haraux, A.1
  • 13
    • 0006989180 scopus 로고    scopus 로고
    • Carleman estimates with the Neumann boundary conditions and its applications to the observability inequality and inverse problems
    • American Mathematical Society Providence, RI
    • V. Isakov, and M. Yamamoto Carleman estimates with the Neumann boundary conditions and its applications to the observability inequality and inverse problems Differential Geometric Methods in the Control of PDE's, Contemporary Mathematics vol. 286 2000 American Mathematical Society Providence, RI 191 227
    • (2000) Differential Geometric Methods in the Control of PDE's, Contemporary Mathematics , vol.286 , pp. 191-227
    • Isakov, V.1    Yamamoto, M.2
  • 15
    • 0000881888 scopus 로고
    • Decay of the solution of the wave equation in a bounded region with boundary dissipation
    • J. Lagnese Decay of the solution of the wave equation in a bounded region with boundary dissipation J. Differential Equations 50 1983 163 182
    • (1983) J. Differential Equations , vol.50 , pp. 163-182
    • Lagnese, J.1
  • 18
    • 0036184704 scopus 로고    scopus 로고
    • Mathematical control theory of coupled PDEs
    • SIAM, Philadelphia
    • I. Lasiecka, Mathematical Control Theory of Coupled PDEs, NSF-CBMS Lecture Notes, SIAM, Philadelphia, 2002.
    • (2002) NSF-CBMS Lecture Notes
    • Lasiecka, I.1
  • 19
    • 0000785441 scopus 로고
    • Nonhomogenous boundary value problems for second order hyperbolic equations
    • I. Lasiecka, J.L. Lions, and R. Triggiani Nonhomogenous boundary value problems for second order hyperbolic equations J. Math Pures Appl. 65 1986 149 192
    • (1986) J. Math Pures Appl. , vol.65 , pp. 149-192
    • Lasiecka, I.1    Lions, J.L.2    Triggiani, R.3
  • 20
    • 84972506618 scopus 로고
    • Uniform boundary stabilization of semi-linear wave equation with nonlinear boundary dissipation
    • I. Lasiecka, and D. Tataru Uniform boundary stabilization of semi-linear wave equation with nonlinear boundary dissipation Differential Integral Equations 6 1993 507 533
    • (1993) Differential Integral Equations , vol.6 , pp. 507-533
    • Lasiecka, I.1    Tataru, D.2
  • 21
    • 0026838533 scopus 로고
    • Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
    • I. Lasiecka, and R. Triggiani Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions Appl. Math. Optim. 25 1992 189 224
    • (1992) Appl. Math. Optim. , vol.25 , pp. 189-224
    • Lasiecka, I.1    Triggiani, R.2
  • 24
    • 0037575409 scopus 로고    scopus 로고
    • A new method to obtain decay estimates for dissipative systems with localized damping
    • P. Martinez A new method to obtain decay estimates for dissipative systems with localized damping Rev. Mat. Comput. 12 1999 251 283
    • (1999) Rev. Mat. Comput. , vol.12 , pp. 251-283
    • Martinez, P.1
  • 25
    • 0033276591 scopus 로고    scopus 로고
    • A new method to obtain decay estimates for dissipative systems
    • P. Martinez A new method to obtain decay estimates for dissipative systems ESAIM Contr. Opt. Calc. Var. 4 1999 419 444
    • (1999) ESAIM Contr. Opt. Calc. Var. , vol.4 , pp. 419-444
    • Martinez, P.1
  • 26
    • 84980140132 scopus 로고
    • Decay of solutions of the wave equation outside nontrapping obstacles
    • C. Morawetz, J. Ralston, and W. Strauss Decay of solutions of the wave equation outside nontrapping obstacles Comm. Pure Appl. Math. 30 1977 447 508
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 447-508
    • Morawetz, C.1    Ralston, J.2    Strauss, W.3
  • 27
    • 0030505515 scopus 로고    scopus 로고
    • Decay of solutions of the wave equation with a local nonlinear dissipation
    • M. Nakao Decay of solutions of the wave equation with a local nonlinear dissipation Math. Ann. 305 1996 403 417
    • (1996) Math. Ann. , vol.305 , pp. 403-417
    • Nakao, M.1
  • 28
    • 0036721224 scopus 로고    scopus 로고
    • Global existence and nonexistence for nonlinear wave equation with damping and source term
    • M. Rammaha, and T. Strei Global existence and nonexistence for nonlinear wave equation with damping and source term Trans. Amer. Math. Soc. 354 2002 3621 3637
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 3621-3637
    • Rammaha, M.1    Strei, T.2
  • 29
    • 12744273003 scopus 로고    scopus 로고
    • Existence for a nonlinear wave equation with damping and source terms
    • J. Serrin, G. Todorova, and E. Vitillaro Existence for a nonlinear wave equation with damping and source terms Integral Differential Equations 16 2003 13 50
    • (2003) Integral Differential Equations , vol.16 , pp. 13-50
    • Serrin, J.1    Todorova, G.2    Vitillaro, E.3
  • 32
    • 0033130609 scopus 로고    scopus 로고
    • Optimalité d'estimation d'énergie pour une équation des ondes amortie
    • J. Vancostenoble Optimalité d'estimation d'énergie pour une équation des ondes amortie C. R. Acad. Sci. Paris Série I 328 1999 777 782
    • (1999) C. R. Acad. Sci. Paris Série i , vol.328 , pp. 777-782
    • Vancostenoble, J.1
  • 33
    • 0034438231 scopus 로고    scopus 로고
    • Optimality of energy estimates for the wave equation with nonlinear boundary velocity damping
    • J. Vancostenoble, and P. Martinez Optimality of energy estimates for the wave equation with nonlinear boundary velocity damping SIAM J. Control 39 2000 776 797
    • (2000) SIAM J. Control , vol.39 , pp. 776-797
    • Vancostenoble, J.1    Martinez, P.2


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